On two-sided infinite fixed points of morphisms

  • Jeffrey Shallit
  • Ming-wei Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)


Let Σ be a finite alphabet, and let h : Σ* → Σ* be a morphism. Finite and infinite fixed points of morphisms — i.e., those words w such that h(w) = w — play an important role in formal language theory. Head characterized the finite fixed points of h, and later, Head and Lando characterized the one-sided infinite fixed points of h. Our paper has two main results. First, we complete the characterization of fixed points of morphisms by describing all two-sided infinite fixed points of h, for both the “pointed” and “unpointed” cases. Second, we completely characterize the solutions to the equation h(xy) = yx in finite words.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jeffrey Shallit
    • 1
  • Ming-wei Wang
    • 1
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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